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Find the greatest common factor.\newline3r3,6r23r^3, 6r^2\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_

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Full solution

Q. Find the greatest common factor.\newline3r3,6r23r^3, 6r^2\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline__\_\_
  1. Factorization of 3r33r^3: First find the complete factorization of 3r33r^3.
    3=33 = 3
    r3=r×r×rr^3 = r \times r \times r
    3r3=3×r×r×r3r^3 = 3 \times r \times r \times r
  2. Factorization of 6r26r^2: Now, find the complete factorization of 6r26r^2.\newline6=2×36 = 2 \times 3\newliner2=r×rr^2 = r \times r\newline6r2=2×3×r×r6r^2 = 2 \times 3 \times r \times r
  3. Find Greatest Common Factor: We found:\newline3r3=3×r×r×r3r^3 = 3 \times r \times r \times r\newline6r2=2×3×r×r6r^2 = 2 \times 3 \times r \times r\newlineFind the greatest common factor of 3r33r^3 and 6r26r^2.\newlineCommon factors are 33, rr, and rr.\newline3×r×r=3r23 \times r \times r = 3r^2\newlineGreatest common factor: 3r23r^2

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